%0 Journal Article %1 Ilin1976Boundary %A Il'in, A. M. %D 1976 %J Mathematics of the USSR-Sbornik %K 35j05-laplacian-operator-helmholtz-poisson-equation 46e35-sobolev-spaces-and-other-spaces-of-smooth-functions %N 4 %T A Boundary Value Problem for the Elliptic Equations of Second Order in a Domain with a Narrow Slit. 1. The Two-Dimensional Case %U https://doi.org/10.1070/SM1976v028n04ABEH001663 %V 28 %X An elliptic equation is considered in a domain \$D\_\varepsilon\$ that is obtained from a two-dimensional domain \$D\$ by removing a neighborhood of a segment. It is assumed that this neighborhood contracts to the segment as \$\varepsilon\to0\$. An asymptotic expansion of the solution of the first boundary value problem in \$D\_\varepsilon\$ is constructed and justified.

@article{Ilin1976Boundary, abstract = {An elliptic equation is considered in a domain \$D\_{\varepsilon}\$ that is obtained from a two-dimensional domain \$D\$ by removing a neighborhood of a segment. It is assumed that this neighborhood contracts to the segment as \$\varepsilon\to0\$. An asymptotic expansion of the solution of the first boundary value problem in \$D\_{\varepsilon}\$ is constructed and justified.}, added-at = {2019-03-01T00:11:50.000+0100}, author = {Il'in, A. M.}, biburl = {https://www.bibsonomy.org/bibtex/2ab4143f2bea79d88acbe8b1e1cfbf292/gdmcbain}, citeulike-article-id = {14677483}, citeulike-linkout-0 = {https://doi.org/10.1070/SM1976v028n04ABEH001663}, interhash = {0ac33bf2f35eefd4d5850ccb2e7205d9}, intrahash = {ab4143f2bea79d88acbe8b1e1cfbf292}, journal = {Mathematics of the USSR-Sbornik}, keywords = {35j05-laplacian-operator-helmholtz-poisson-equation 46e35-sobolev-spaces-and-other-spaces-of-smooth-functions}, number = 4, posted-at = {2019-01-07 23:14:59}, priority = {1}, timestamp = {2019-03-01T00:11:50.000+0100}, title = {{A Boundary Value Problem for the Elliptic Equations of Second Order in a Domain with a Narrow Slit. 1. The Two-Dimensional Case}}, url = {https://doi.org/10.1070/SM1976v028n04ABEH001663}, volume = 28, year = 1976 }